Yau's Affine-Normal Descent for Large-Scale Unrestricted Higher-Moment Portfolio Optimization

Battle Count: 78

Highly relevant to quantitative trading and portfolio management. The paper directly addresses the computational bottleneck preventing large-scale MVSK portfolio optimization, making it feasible to compare higher-moment portfolios with exact mean-variance portfolios across thousands of assets. The economic findings (higher moments matter most at moderate return targets, not aggressive ones) provide actionable guidance for portfolio construction. The method enables full-universe comparisons on 5-minute intraday data for 5,440 stocks, which is directly applicable to institutional portfolio management and quantitative strategy design. However, the static allocation design and market-window dependence limit immediate deployment as a trading system.

High implementation complexity. The solver requires: (1) exact sample-oracle kernels for value, gradient, Hessian-vector products, and third-order directional actions computed via matrix-vector operations with the centered return matrix A; (2) reduced-coordinate representation on the simplex tangent space using an orthonormal basis U; (3) Householder frame construction for the affine-normal direction; (4) regularized tangent linear system solve (direct or PCG-based); (5) exact quartic line search from mixed sample power sums with cubic-root computation; (6) simplex boundary handling with interior slice, projected trial steps, and active-face continuation; (7) stall-recovery restarts for the PCG configuration. The theoretical framework involves affine differential geometry, Polyak-Lojasiewicz inequalities, and curvature decomposition. However, the paper notes the project-specific implementation burden is relatively modest (an oracle adapter and simplex wrapper on top of a matrix-free YAND routine).

The paper states a replication package will provide code, README, and scripts for synthetic experiments. However, the real-data analysis uses licensed RESSET intraday data that cannot be redistributed; only data-construction code and instructions for reconstruction from an authorized RESSET license will be provided. No GitHub repository URL is given. The algorithmic details, parameter settings, and oracle formulas are thoroughly documented in the main text and appendices, enabling independent implementation.